Transpose s=ut+1/2at^2?

Question

I have been given this equation can anyone manage to correctly transpose it for t and show me the working out and answer in plain english step by step?

Thanks x

Answer 1

ok, sorry many answering aren't really helping you. This is a quadratic equation in t, which we can re-write as:

(1/2)a(t^2)+ut-s=0 and we need to solve for t

Do you know the quadratic formula? I'll give it to you here and we will apply it to the above expression.

Given A(x^2)+Bx+C=0 the solutions for x is:

x= -B/2A + {(B^2-4AC)^(1/2)}/2A and

x= -B/2A - {(B^2-4AC)^(1/2)}/2A

or replacing for what you have above this gives:

A=(a/2), B=u, c=-s, x=t

t= -u/a + {(u^2+2as)^(1/2)}/a and

t= -u/a - {(u^2+2as)^(1/2)}/a

This equation is also the equation of motion with t as time, a as acceleration, and u as velocity! In that case we only want the positive value for t, or the first one we wrote! Hope this helped!

Answer 2

s=ut+1/2at^2
0 = 1/2at^2 + ut - s --- get everything to one side
0 = at^2 + 2ut - 2s --- multiply by 2 to get rid of fraction

t = {- 2u +- SQRT [(2u)^2 - 4(a)(-2s)]} / (2a)
--- using the method for solving quadratic equations

t = {- 2u +- SQRT [4u^2 + 8as]} / (2a)

I feel that if you were to substitue the values for s (displacement), u (initial velocity) and a (gravitational accaleration, 10 or 9.81 m/s2), you will find it easier to solve as the algebraic expressions can make the sum look harder than it really is.

Answer 3

s=ut+1/2at^2
2s=2ut+at^2
at^2+2ut-2s=0
this is now in the form of a
standard quadratic
use the formula:
t= {-2u+/-sqrt(4u^2+8as)}/2a
={-2u+/-sqrt(4(u^2+2as))}/2a
={-u+/-sqrt(u^2+2as)}/a

i hope that this helps

Answer 4

s=ut+(1/2)at^2
s=(1/2)at^2+ut

Multiply both sides by (2/a)
2s/a=t^2+ut/a

Now add (u/a)^2 to both sides
2s/a+(u/a)^2=t^2+ut/a+(u/a)^2

Now factor the right hand side
2s/a+(u/a)^2=(t+u/a)^2

Take the square root of both sides:
(2s/a+(u/a)^2)^(1/2)=t+u/a

Subtract u/a from both sides:
(2s/a+(u/a)^2)^(1/2)-u/a=t

Note that ^(1/2) is the same as square root

Answer 5

multiply through out by 2
at^2+2ut-2s=0
t=[-2u+/-rt(4u^2+8as)]/2a

Answer 6

I've had a few beers, so it's probably wrong, and why am I doing it at all, but

Ok, now I've read it sober, I'll take away my answer.

Can't you post questions like this earlier in the evening? :)